A very quick search suggests that earth will become uninhabitable somewhere between 500 million and 2 billion years from now. If we shot a probe to this life-friendly alien planet with some sort of primordial soup, even traveling at the speed of light it would take 4 billion earth years to get there. Do I have that right? Basically we'll never even come close to being around when it finally arrives, if it ever arrive…
Mars has a leaky atmosphere - sure it's a real fixer upper. But we have a better chance of fixing it, or even correcting the orbit of our planet so that in 500 million years it's still livable.